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This biographical sketch is well-written, concise, and complete (or at least it appears to be). It includes many quotes and photos that I hadn’t seen before. B

This biographical sketch is well-written, concise, and complete (or at least it appears to be). It includes many quotes and photos that I hadn’t seen before. But I can imagine that some readers will be left wondering what was so remarkable about this guy’s work. Unfortunately, it’s hard to explain without some exposure to pure mathematics. David Mumford, who pops up in this article, has a lengthy blog post[1] on this exact problem, stemming from his experience writing Grothendieck’s obituary for Nature. It’s an interesting read if you have some math background. In any case, I think the New York Times obituary by Edward Frenkel[2] does a nice job of giving a taste of his work to a lay audience (by tackling the problem of defining Grothendieck’s schemes, just like Mumford did). [1] http://www.dam.brown.edu/people/mumford/blog/2014/Grothendieck.html http://www.dam.brown.edu/people/mumford/blog/2014/Grothendie... [2] https://www.nytimes.com/2014/11/25/science/the-lives-of-alexander-grothendieck-a-mathematical-visionary.html https://www.nytimes.com/2014/11/25/science/the-lives-of-alex...

mikorym 7y ago
And for the more nonlay audience, Grothendieck's real pull is the persistence with which he applied category theoretic techniques successfully. Usually one would qualify this to algebraic geometry, but I think his approach can be followed in any of the many extensive fields in mathematics. I would contrast this to what often happens in the physics community, albeit not in a condescending manner, where techniques diverge rather than converge. In fact, I would guess this is the role that Einstein played a hundred years ago: to encourage sensible connections between researchers' work.
- nabla9 7y ago
  Grothendieck's relative point of view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_point_of_view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_poin...
  - mikorym 7y ago
    Linked to via two degrees is this: https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem#/media/File:Grothendieck-Riemann-Roch.jpg https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E.... I don't know German, but it would be really interesting to know what the text says.
    - detaro 7y ago
      rough translation (it's kinda tricky to preserve the tone. Question marks are words I'm not sure the translation works): > Riemann-Roch theorem: the last trend(?): the diagram(?) <formula> is commutative! To give this statement over f:x->y an approximative sense I had try the patience of the listeners for almost 2 hours. Black-on-white (in Springer's Lecture Notes) its about 400, 500 pages. A fitting example how our drive to knowledge and discovery more and more realizes itself in a far-from-life logical delirium, while the life itself is ruined in a thousand ways - and is threatened by total destruction. High time to change our path!
      - mikorym 7y ago
        I wonder if he means what I think he means, which is that a concept that is for some field all-encompassing in your mind takes 400 pages to write down in a way that translates your ideas. University group theory is like that, when the real objective may just be to show that you can't circle the square.
nikofeyn 7y ago
> Unfortunately, it’s hard to explain without some exposure to pure mathematics. you are right, but i suspect that is still a massive understatement. thanks for the links.

mikorym 7y ago

And for the more nonlay audience, Grothendieck's real pull is the persistence with which he applied category theoretic techniques successfully. Usually one would qualify this to algebraic geometry, but I think his approach can be followed in any of the many extensive fields in mathematics. I would contrast this to what often happens in the physics community, albeit not in a condescending manner, where techniques diverge rather than converge. In fact, I would guess this is the role that Einstein played a hundred years ago: to encourage sensible connections between researchers' work.

nabla9 7y ago
Grothendieck's relative point of view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_point_of_view https://en.wikipedia.org/wiki/Grothendieck%27s_relative_poin...
- mikorym 7y ago
  Linked to via two degrees is this: https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E2%80%93Roch_theorem#/media/File:Grothendieck-Riemann-Roch.jpg https://en.wikipedia.org/wiki/Grothendieck%E2%80%93Riemann%E.... I don't know German, but it would be really interesting to know what the text says.
  - detaro 7y ago
    rough translation (it's kinda tricky to preserve the tone. Question marks are words I'm not sure the translation works): > Riemann-Roch theorem: the last trend(?): the diagram(?) <formula> is commutative! To give this statement over f:x->y an approximative sense I had try the patience of the listeners for almost 2 hours. Black-on-white (in Springer's Lecture Notes) its about 400, 500 pages. A fitting example how our drive to knowledge and discovery more and more realizes itself in a far-from-life logical delirium, while the life itself is ruined in a thousand ways - and is threatened by total destruction. High time to change our path!
    - mikorym 7y ago
      I wonder if he means what I think he means, which is that a concept that is for some field all-encompassing in your mind takes 400 pages to write down in a way that translates your ideas. University group theory is like that, when the real objective may just be to show that you can't circle the square.

nikofeyn 7y ago

> Unfortunately, it’s hard to explain without some exposure to pure mathematics. you are right, but i suspect that is still a massive understatement. thanks for the links.